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Related papers: Scaling and Crossovers in Diffusion Limited Aggreg…

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We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that…

Statistical Mechanics · Physics 2009-11-11 Leonard M. Sander , Ellak Somfai

Diffusion-limited aggregation (DLA) assumes that particles perform pure random walk at a finite temperature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a…

Statistical Mechanics · Physics 2013-09-02 Li Deng , Yanting Wang , Zhong-Can Ou-Yang

We study the structure and growth of a difusion-limited aggregate (DLA) for which the constitutive units remain mobile during the aggregation process. Contrary to DLA where far from equilibrium conditions are the prevalent factor for…

Statistical Mechanics · Physics 2009-11-10 Carlos I. Mendoza , Carlos M. Marques

Discrete scale invariance, which corresponds to a partial breaking of the scaling symmetry, is reflected in the existence of a hierarchy of characteristic scales l0, c l0, c^2 l0,... where c is a preferred scaling ratio and l0 a microscopic…

Statistical Mechanics · Physics 2015-06-25 A. Johansen , D. Sornette

Diffusion-limited aggregation is consistent with simple scaling. However, strong subdominant terms are present, and these can account for various earlier claims of anomalous scaling. We show this in detail for the case of multiscaling.

Statistical Mechanics · Physics 2007-05-23 Ellak Somfai , Robin C. Ball , Neill E. Bowler , Leonard M. Sander

We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to alpha^{-n}, where alpha<1 is a positive real parameter. The heights of these…

Probability · Mathematics 2007-05-23 MArtin T. Barlow , Robin Pemantle , Edwin A. Perkins

In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter $\lambda$, which…

Statistical Mechanics · Physics 2009-11-11 S. C. Ferreira , S. G. Alves , A. Faissal Brito , J. G. Moreira

We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when…

Probability · Mathematics 2011-11-21 Amine Asselah , Alexandre Gaudilliere

The dynamical properties of the invasion percolation on the square lattice are investigated with emphasis on the geometrical properties on the growing cluster of infected sites. The exterior frontier of this cluster forms a critical loop…

Statistical Mechanics · Physics 2020-12-02 S. Tizdast , N. Ahadpour , M. N. Najafi , Z. Ebadi , H. Mohamadzadeh

In the classical model of Diffusion Limited Aggregation (DLA), introduced by Witten and Sander, the process begins with a single particle cluster placed at the origin of a space, and then, one at a time, particles make a random walk from…

Probability · Mathematics 2026-04-29 Colin Cooper , Alan Frieze

We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this…

Probability · Mathematics 2013-06-20 Gideon Amir , Omer Angel , Gady Kozma

The paper suggests a generalisation of the diffusion-limited aggregation (DLA) based on using a general stochastic process to control particle movements before sticking to a growing cluster. This leads to models with variable…

Statistical Mechanics · Physics 2007-05-23 Ilya Molchanov

Results from a modified Diffusion Limited Aggregation (DLA) model are presented. The modifications of the classical DLA model are in the attachment to the cluster rules and in the scheme of particle generation/killing. In the classical DLA…

Mesoscale and Nanoscale Physics · Physics 2011-05-30 Bogdan Ranguelov , Desislava Goranova , Vesselin Tonchev , Rositsa Yakimova

We study conserved one-dimensional models of particle diffusion, attachment and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) ~ m^{-k}, k>0. Heuristic scaling arguments based on…

Statistical Mechanics · Physics 2009-11-13 F. D. A. Aarao Reis , R. B. Stinchcombe

Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…

Statistical Mechanics · Physics 2015-06-19 Hiroshi Miki

Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban…

Condensed Matter · Physics 2007-05-23 Hernan A. Makse , Shlomo Havlin , H. Eugene Stanley

We propose a simple model of columnar growth through {\it diffusion limited aggregation} (DLA). Consider a graph $G_N\times\N$, where the basis has $N$ vertices $G_N:=\{1,\dots,N\}$, and two vertices $(x,h)$ and $(x',h')$ are adjacent if…

Probability · Mathematics 2015-11-24 A. Asselah , E. Cirillo , E. Scoppola , B. Scoppola

Internal DLA (IDLA) is an internal aggregation model in which particles perform random walks from the origin, in turn, and stop upon reaching an unoccupied site. Levine and Peres showed that, when particles start instead from fixed…

Probability · Mathematics 2022-01-24 David Darrow

A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are…

Soft Condensed Matter · Physics 2009-11-13 Patrick B. Warren

Internal Diffusion Limited Aggregation (IDLA) is a model that describes the growth of a random aggregate of particles from the inside out. Shellef proved that IDLA processes on supercritical percolation clusters of integer-lattices fill…

Probability · Mathematics 2011-11-03 Hugo Duminil-Copin , Cyrille Lucas , Ariel Yadin , Amir Yehudayoff